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Spillways Hoover dam
goal: deliver high discharge protecting dams from uncontrolled overtopping. Localized high velocity and large elevation range
design strategy for the concrete ogee spillway: keep atm. pressure on the spillway surface, as for a sharp crested weir. same hydrodynamics NOTE: the head H is differently evaluated H vs H’
L 2/3CLHQ
stronger structure
As compared to the lower nappe profile (no ogee), we may have a steeper (e.g for H<Hdesign) or a more shallow (e.g for H>Hdesign) profile
pressure is larger than atm. drag and lower Q flow separation
occurs low pressure at the surface cavitation
on the discharge coefficient....
for P/H>>1 (high spillways) we can consider the spillway as a sharp crested weir
gC
from
P
Hwith
LHCgQ
d
d
23
2C estimate we
CLHQ
728.0C
H'89.0Hfor
611.008.0611.0'C
''23
2
3/2
d
d
2/3
QUALITATIVELY QUANTITATIVELY
Define L based on abutment and contractions: BB 3
note : lower H imposes a higher cd for the same discharge
upstream face slope and different geometries for the ogee
For low spillways Cd depends on pressure, total head, upstream face slope
P
H08.0611.0'C d
the lower nappe (sharp crested weir) change with the design head Hd
H>Hd
p<patm
cavit.
H<Hd
p>patm
drag
Therefore the discharge coefficient for each actual head values He will vary (while Hd and thus the ogee shape are fixed)
Example : given P/Hd=0.67 and He/Hd=1 we have C/C0~0.96 however if He/Hd=1.2 we have C/C0~0.99 3% more in discharge, but increased chance of cavitation damages How do we quantify the risk of cavitation ?
How do we quantify the risk of cavitation ? We accept a certain risk by tolerating a certain low pressure e.g. constraining hp/Hd > - 0.2 we must keep H/Hd < 1.33 This rule defines the design head Hd based on hydrologic prediction
low pressure peak at x/Hd=-0.2
Note that for Hd=He the pressure is ~ atmospheric
Given a design head Hd we obtain the constraint for the operational regime of the spillway: for larger design head, and limit cavitation zone (hp= p/ <-25ft), we have to be more careful He is the maximum head for a given design condition
EXAMPLE 4
Note that cavitation occurs for hp= p/ <-25 ft
Further reading:
spillway aeration avoid localized cavitation, increase discharge coeff. without smoothing surface
introducing air at atmospheric pressure , or making sure that the flow will entrain air (self-aeration for long spillways), reduces low pressure at the spillway surface and avoid cavitation
stepped versus smooth spillways http://www.flow3d.com/resources/news_12/spring/simulating-flow-over-stepped-spillways.html
En. dissipation estimates
N Number step, h step height: large N, low H >> smooth spillway
yc/h>0.8 skimming